Some consequences of perversity of vanishing cycles

Details Some consequences of perversity of vanishing cycles Some consequences of perversity of vanishing cycles

2003-08-08

arxiv.org/abs/math/0308078v4

Mathematics

Algebraic Geometry

20 pages, minor change

Scientific paper

For a holomorphic function on a complex manifold, we show that the vanishing
cohomology of lower degree at a point is determined by that for the points near
it, using the perversity of the vanishing cycle complex. We calculate it
explicitly in the case the hypersurface has simple normal crossings outside the
point. We also give some applications to the monodromy.

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